最小二乘二维圆拟合方法在海上风电打桩垂直度监测中的应用

The method of least square two-dimensional circle fitting in perpendicularity surveying of offshore wind power piling

海上风电单桩基础垂直度监测,通常依靠“水平尺法”和“经纬仪扫边法”两种测量方式。受制于没有严密的数学算法作为支撑,此两种方法均不能得到科学严谨的测量数值,只能作为施工中的辅助参考。利用钢管桩为标准圆形的特性,提出了一种利用“上下截面圆拟合”计算垂直度的新方法,论证了二维水平圆拟合在垂直度监测中的可行性。根据观测点距圆心距离的平方和为最小的特性,推导了基于二维水平圆拟合的最小二乘法公式,并对公式进行了线性化处理,便于进行计算机编程等软件开发。将本文算法在海上风电场施工中进行了实际检验应用,与最终验收测量结果进行了比对,拟合计算得钢管桩垂直度为p=3.056‰,电子水准验收测量得垂直度p=3.012‰,验证了算法的精确度和可靠性。

The verticality monitoring of single pile foundation of offshore wind power usually relies on two measuring methods:"level method"and"theodolite sweep method".Due to the lack of strict mathematical algorithm as the support,these two methods can not get scientific rigorous measurement values,but can only be used as auxiliary reference in construction.Based on the characteristic that steel pipe is a standard circle,a new method of calculating verticality by"upper and lower section circle fitting"was proposed,and the feasibility of two-dimensional horizontal circle fitting in verticality monitoring was demonstrated.According to the property that the sum of the squares of the distance between the observation point and the center of the circle was the minimum,the least square formula based on two-dimensional horizontal circle fitting was derived,and the formula was linearized,which was convenient for computer programming and other software development.The proposed algorithm was tested and applied in the construction of offshore wind farm,and compared with the final acceptance measurement results.The verticality of steel pipe pile calculated by fitting total was p=3.056‰,and the verticality measured by electronic leveling acceptance was p=3.012‰,which verified the accuracy and reliability of the algorithm.